The PSG is one of the symmetry groups of the Platonic solids.
There are three polyhedral groups: the tetrahedral group
of order 12, the octahedral group of order 24, and the
icosahedral group of order 60.

All doctests have been given in the docstring of the
constructor of the object.

Apply a permutation to the polyhedron in place. The permutation
may be given as a Permutation instance or an integer indicating
which permutation from pgroup of the Polyhedron should be
applied.

This is an operation that is analogous to rotation about
an axis by a fixed increment.

Notes

When a Permutation is applied, no check is done to see if that
is a valid permutation for the Polyhedron. For example, a cube
could be given a permutation which effectively swaps only 2
vertices. A valid permutation (that rotates the object in a
physical way) will be obtained if one only uses
permutations from the pgroup of the Polyhedron. On the other
hand, allowing arbitrary rotations (applications of permutations)
gives a way to follow named elements rather than indices since
Polyhedron allows vertices to be named while Permutation works
only with indices.